Found 29 Documents (Results 1–29)
Parallelohedra, old and new. (English) Zbl 07878987
On Voronoi’s conjecture for four- and five-dimensional parallelohedra. (English. Russian original) Zbl 1489.52012
Russ. Math. Surv. 77, No. 1, 174-176 (2022); translation from Usp. Mat. Nauk 77, No. 1, 185-186 (2022).
Reviewer: Lionel Pournin (Paris)
An isoperimetric problem for three-dimensional parallelohedra. (English) Zbl 1490.52014
Reviewer: Elizaveta Zamorzaeva (Chişinău)
Smallest polyhedral tilings of 3-tori by parallelohedra. (English) Zbl 1467.52028
Reviewer: Elizaveta Zamorzaeva (Chişinău)
Embedding parallelohedra into primitive cubic networks and structural automata description. (English) Zbl 07872875
On the \(\Sigma\) classes in \(E^6\). (English) Zbl 07872868
MSC:
52C23
On the density of sets avoiding parallelohedron distance 1. (English) Zbl 1430.52022
Reviewer: László A. Székely (Columbia)
A class of affinely equivalent Voronoi parallelohedra. (English. Russian original) Zbl 1316.52003
Math. Notes 95, No. 5, 625-633 (2014); translation from Mat. Zametki 95, No. 5, 697-707 (2014).
MSC:
52A20
Atoms for parallelohedra. (English) Zbl 1319.52026
Bárány, Imre (ed.) et al., Geometry – intuitive, discrete, and convex. A tribute to László Fejes Tóth. Berlin: Springer; Budapest: János Bolyai Mathematical Society (ISBN 978-3-642-41497-8/hbk; 978-3-642-41498-5/ebook). Bolyai Society Mathematical Studies 24, 23-43 (2013).
MSC:
52C22
On the enumeration of the combinatorial types of primitive parallelohedra in \(E^{d}\), \(2 \leq d\leq 6\). (English) Zbl 1284.05134
Parallelohedra: a retrospective and new results. (English. Russian original) Zbl 1271.52013
Trans. Mosc. Math. Soc. 2012, 207-220 (2012); translation from Tr. Mosk. Mat. O.-va 73, No. 2, 259-276 (2012).
The similarity types of primitive parallelohedra in \(E^d\), \(2 \leq d\leq 5\). (English) Zbl 1243.52009
On polyhedra with centrally symmetric faces. (Russian) Zbl 1280.52013
MSC:
52B15
On the cone of positive-definite quadratic forms. (English) Zbl 1333.52014
Laurinčikas, Antanas (ed.) et al., Voronoï’s impact on modern science. Book 4, Volume 1. Proceedings of the 4th international conference on analytic number theory and spatial tessellations, Kyiv, Ukraine, September 22–28, 2008. Kyiv: Institute of Mathematics, NAS of Ukraine (ISBN 978-966-02-4891-5/pbk; 978-966-02-4890-8/set). 220-232 (2008).
On zonohedral parallelohedra. (English) Zbl 1142.52301
Syta, H. (ed.) et al., Voronoï’s impact on modern science. Book III. Proceedings of the 3rd Voronoï conference on analytic number theory and spatial tessellations. Kyiv: Institute of Mathematics (ISBN 966-02-2571-7; 966-02-3764-2). Proceedings of the Institute of Mathematics of the National Academy of Sciences of Ukraine, Mathematics and its Applications 55, 109-125 (2005).
MSC:
52B12
On \(C\)-types of positive definite quadratic forms. (English) Zbl 1044.11058
Dubickas, A. (ed.) et al., Analytic and probabilistic methods in number theory. Proceedings of the third international conference in honour of J. Kubilius, Palanga, Lithuania, September 24–28, 2001. Vilnius: TEV (ISBN 9955-491-30-2/hbk). 320-328 (2002).
Reviewer: Guram Gogishvili (Tbilisi)
Solution of the basic problems of discrete geometry on the plane. (English) Zbl 0986.11043
Bambah, R. P. (ed.) et al., Number theory. Basel: Birkhäuser. Trends in Mathematics. 401-461 (2000).
Reviewer: Ranjeet Sehmi (Chandigarh)
On rhombic dodecahedra. (English) Zbl 0973.52014
Reviewer: William Moser (Montréal)
The extension theorem. (English) Zbl 0970.52011
Reviewer: Egon Schulte (Boston)
New investigations of parallelohedra in \(R^{d}\). (English) Zbl 0955.51011
Engel, P. (ed.) et al., Voronoï’s impact on modern science. Book II. Transl. from the Ukrainian. Kyiv: Institute of Mathematics. Proc. Inst. Math. Natl. Acad. Sci. Ukr., Math. Appl. 21(2), 22-60 (1998).
The Warsaw period of Voronoï’s creative work. (English) Zbl 0952.01036
Engel, P. (ed.) et al., Voronoï’s impact on modern science. Book I. Transl. from the Ukrainian. Kyiv: Institute of Mathematics. Proc. Inst. Math. Natl. Acad. Sci. Ukr., Math. Appl. 21(1), 29-33 (1998).
Reviewer: Eugène Dubois
The structure of primitive parallelohedra and Voronoi’s last problem. (English. Russian original) Zbl 0927.51028
Russ. Math. Surv. 53, No. 2, 403-405 (1998); translation from Usp. Mat. Nauk 53, No. 2, 161-162 (1998).
MSC:
51M20
A new family of trivalent space-filling parallelohedra. (English) Zbl 0659.51025
Reviewer: E.Hertel
\(C\)-types of \(n\)-dimensional lattices and 5-dimensional primitive parallelohedra (with application to the theory of coverings). (English. Russian original) Zbl 0419.10031
Proc. Steklov Inst. Math. 137, 140 p. (1976); translation from Tr. Mat. Inst. Steklov 137, 131 p. (1976).
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